Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 801 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 18 (d) 20
2. 2.A drawer has lots of blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 2 (d) 5
3. 3.A drawer has lots of red, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 4 (c) 2 (d) 3
4. 4.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 240 (d) 25
5. 5.3 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 24 (c) 10 (d) 21
6. 6.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 55 (c) 110 (d) 66
7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 17 (d) 19
8. 8.In a class of 46 children, 28 like cricket, 26 like football and 1 like neither. How many like both? (a) 8 (b) 45 (c) 1 (d) 9
9. 9.The mean of 8 numbers is 15. When the number 33 is added to them, what is the new mean? (a) 17 (b) 15 (c) 18 (d) 24
10. 10.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 8010 (c) 3916 (d) 4005
11. 11.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
12. 12.What are the roots of x² − 16x + 63 = 0? (a) 3 and 21 (b) 1 and 15 (c) 1 and 63 (d) 7 and 9
13. 13.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 648 (c) 1332 (d) 630
14. 14.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 14 (d) 21
15. 15.A bag has 4 white balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 5 (c) 2 (d) 15
16. 16.If a + b = 20 and ab = 99, what is a² + b²? (a) 400 (b) 301 (c) 598 (d) 202
17. 17.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 3/5 (d) 1/4
18. 18.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 16 (c) 24 (d) 12
19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
20. 20.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
21. 21.What is the 33rd term of the AP 16, 22, 28, 34, …? (a) 198 (b) 208 (c) 192 (d) 214
22. 22.A bag has 3 green, 2 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/8 (b) 1/3 (c) 1/4 (d) 3/4
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
24. 24.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 160°
25. 25.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
26. 26.What are the roots of x² − 5x + 6 = 0? (a) 1 and 6 (b) 2 and 3 (c) 2 and 4 (d) 1 and 4
27. 27.In which quadrant does the point (3, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 6 (b) 3 (c) 4 (d) 5
29. 29.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
30. 30.What is the smallest prime factor of 57? (a) 19 (b) 3 (c) 1 (d) 2
31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 17 (d) 16
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/11 (c) 3/11 (d) 1/9
34. 34.What is the distance between the points (5, 8) and (11, 0)? (a) 14 (b) 100 (c) 10 (d) 11
35. 35.In a class of 35 children, 21 like cricket, 15 like football and 1 like neither. How many like both? (a) 3 (b) 34 (c) 2 (d) 1
36. 36.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 13 (b) 15 (c) 4 (d) 14
38. 38.A drawer has lots of black, red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 3 (d) 4
39. 39.How many factors does 116 have? (a) 7 (b) 5 (c) 4 (d) 6
40. 40.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm

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